How the Anderson-Darling statistic is used to assess the distribution fit

The Anderson-Darling (AD) statistic measures how well the data follow a particular distribution. Generally, the better the distribution fits the data, the smaller the AD statistic is.

The AD statistic is used to calculate the p-value for the goodness-of-fit test, which helps you determine which distribution best fits your data. For example, the AD statistic is calculated for each distribution when you perform Individual Distribution Identification. The p-values calculated from the statistic helps you determine which distribution model to use for a capability analysis or a reliability analysis. The AD statistic is also used to test whether a sample of data comes from a population with a specified distribution. For example, you may need to test whether your data meet the assumption of normality for a t-test.

The hypotheses for the Anderson-Darling test are:
  • H0: The data follow a specified distribution.
  • H1: The data do not follow a specified distribution.

If the p-value for the Anderson-Darling test is lower than the chosen significance level (usually 0.05 or 0.10), conclude that the data do not follow the specified distribution. Minitab does not always display a p-value for the Anderson-Darling test because it does not mathematically exist for certain cases.

If you are comparing the fit of several distributions, the distribution with the largest p-value usually has the closest fit to the data. If distributions have similar p-values, choose one of the distributions based on practical knowledge.

Some commands generate an adjusted Anderson-Darling, or AD*, statistic. The non-adjusted Anderson-Darling statistic uses the nonparametric step function based on the Kaplan-Meier method of calculating plot points, while the adjusted Anderson-Darling statistic uses other methods to calculate the plot points.